This invention relates generally to industry solutions for the Energy & Utility (E&U) industry and more particularly to E&U operation and planning studies involving optimal power flow.
This section is intended to provide a background or context to the invention disclosed below. The description herein may include concepts that could be pursued, but are not necessarily ones that have been previously conceived, implemented or described. Therefore, unless otherwise explicitly indicated herein, what is described in this section is not prior art to the description in this application and is not admitted to be prior art by inclusion in this section.
Central to an E&U's daily operation and planning studies is to solve an optimal power flow (OPF) problem under various constraints (e.g., primary electrical power flow constraints). For instance, one question commonly posed is, what is the most economical generation dispatch schedule under those electrical power flow constraints?
Because of its complexity, OPF is typically solved approximately. As an example, alternating current (AC) power flow constraints are approximated by their direct current (DC) power flow constraints. Thus, the nonlinear optimization problem becomes a linear programming problem, which is relatively easy to solve.
Direct consideration of AC power flow constraints has high computation complexity. Particularly, constraints, Jacobian functions and Hessian functions need to be computed explicitly either through closed formulas (e.g., MatPower, which is a MATLAB power system simulation package) or automatic differentiation. The latter is described, e.g., by Jiang et al., “An Efficient Implementation of Automatic Differentiation in Interior Point Optimal Power Flow”, IEEE Transactions on Power Systems, Vol. 25, No. 1, February 2010. See also Prasad Raju, et al., “An efficient technique of calculating first and second order derivatives in newton based optimal power flow problem,” International Journal of Research & Reviews in Computer Science, June 2012, Vol. 3 Issue 3, p1645.
Problems with these approaches include that either the solution quality is low as an approach uses approximated electrical models, or the performance is low with high computation cost.